SUMMARY Carbon capture and storage (CCS) within sealed geological formations is an essential strategy to reduce global greenhouse gas emissions, the primary goal of the 2015 United Nations Paris Agreement. Large-scale commercial development of geological CO2 storage requires high-resolution remote sensing methods to monitor CO2 migration during/after injection. A geological formation containing a CO2 phase in its pore space commonly exhibits higher electrical resistivity than brine-saturated (background) sediments. Here, we explore the added value of the marine controlled-source electromagnetic (CSEM) method as an additional and relevant geophysical tool to monitor moderate to significant changes in CO2 saturation within a fluid conduit breaking through the seal of a CCS injection reservoir, using a suite of synthetic studies. Our 2-D CSEM synthetic models simulate various geological scenarios incorporating the main structural features and stratigraphy of two North Sea sites, the Scanner Pockmark and the Sleipner CCS site. Our results show significant differentiation of leakage through the seal with CO2 saturation ($S_{{\rm CO}_2}$) ranging between 20 and 50 per cent, while our rock physics model predicts that detection below 20 per cent would be challenging for CSEM alone. However, we are able to detect with our 2-D inversion models the effects of saturation with 10 and 20 per cent CO2 within a chimney with 10 per cent porosity. We demonstrate that simultaneous inversion of Ey and Ez synthetic electric field data facilitates a sharper delineation of a CO2 saturated chimney structure within the seal, whereas Ez synthetic data present higher sensitivity than Ey to $S_{{\rm CO}_2}$ variation, demonstrating the importance of acquiring the full 3-D electric field. This study illustrates the value of incorporating CSEM into measurement, monitoring and verification strategies for optimal operation of marine CCS sites.